Yes, but that's not easy... I can't remember exactly, but I think I saw an estimate that the compute time to train just one of the GPT models cost around $66 million. IDK whether that's total cost from scratch, or incremental cost to arrive at that model starting from an earlier model that was already built, but I do know that GPT is still to this day using that September 2021 cutoff which to me kind of implies that they're building progressively on top of already-assembled models and datasets (which makes sense, because to start from scratch without needing to would be insane).

You could, technically, start from scratch and spend 2 more years and however many million dollars retraining a new model that doesn't have the private data you're trying to excise, but I think the point the article is making is that that's a pretty difficult approach and it seems right now like that's the only way.